What does standard mean in math?

Answer 1

Standard has several different meanings in mathematics - depending on the context. In general, it refers to something that has an agreed form or value, or measures that have been adjusted to remove some systematic scaling factor.

The SI (International Standard) units: Kilometer, Gram, Second are an example of measurement units that are agreed across the world - including within the scientific community in some recalcitrant countries.

There are the standard equation of a straight line ax + by = k, where x and y are the coordinate variables and a, b and k are constants. Unlike the slope intercept form, the standard form can easily be extended to 3-dimensional space thus:

ax + by + cz = k with z as another coordinate and c as another constant. Extending to more dimensions is carried out similarly.

In statistics there is the standard normal distribution which is the normal (Gaussian) distribution that has been translated and rescaled so that its mean is zero and its variance is 1.

Finally, there is the standard notation which, unfortunately, is not a standard term. Some people use it to mean the "normal" way of writing numbers while others use the terms to mean scientific notation.